But actions speak louder than words. And when it comes to action, unfortunately these companies fail miserably.

They not only continue to produce and invest in fossil fuels, but they also refuse to heed growing concern from shareholders about the impact climate change may have on their operations. No example makes that position more clear than their respective boards' position on some common-sense shareholder resolutions.

“In preparation for their annual meetings on May 31, both Chevron and ExxonMobil opposed every climate-related resolution put forth by their shareholders,” Kathy Mulvey, with the Union of Concerned Scientists, wrote in a blog post this week.

Both companies are facing unprecedented shareholder concern with respect to climate change. And it's not just the climate activists who are calling on companies like Exxon to change. Some major investors are also joining the call. Aegon Asset Management, which manages $10 billion in assets, is one of many companies asking the company to disclose the resilience of its portfolio – a common-sense, risk-abatement strategy that more and more investors should consider.

What’s concerning to these investors is that Exxon and Chevron are even lagging behind other oil companies.

"While European companies such as Shell, Anglo American and Rio Tinto have embraced these resolutions, U.S. companies have been more resistant," Natalie Beinisch, an engagement officer with Aegon Asset Management, said in a press statement last month.

Despite this astounding alliance between environmental activists and big finance, Exxon and Chevron seem reticent to consider climate change in their future planning.

So, what can we do? One idea: divest. The New York City Employee Retirement System has approximately $321 million invested in Exxon and $169 million invested in Chevron alone, according to Go Fossil Free. They -- and other big-money systems -- could send a strong message to the two companies ahead of their annual meetings.

“For a city that prides itself on being a frontrunner, New York is quickly falling behind when it comes to investing in a climate-friendly future," said Jamie Tyberg, with New York Communities for Change, in a press statement.

A similar climate resilience resolution targeting Exxon got 38 percent support last year. And it remains to be seen if the support of companies like Aegon will push this year's resolution above 50 percent.

But chances are, Exxon will just ignore the evidence as they have for decades. Winning a single shareholder resolution won't change the practices of a company whose entire business is built upon denial and producing dirty fossil fuels.

Perhaps Exxon and Chevron won't listen to shareholders when they advocate at annual meetings. But I have a feeling they'll notice when more and more cities, funds, and investors divest and impact share prices. Then, maybe, they'll finally start to take climate change seriously – but I wouldn't count on it.